The Sovereignty of Nations

by

Kyle Bagwell and Robert W. Staiger*

First Draft: May 2003

Revised: September 2003

*Bagwell: Columbia University and NBER; Staiger: University of Wisconsin and NBER. We thank

Alberto Martin and especially Stephen Krasner for many helpful comments, and the National

Science Foundation for support.

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“Of all the rights possessed by a nation, that of sovereignty is doubtless the most important.” Emmerich de Vattel in TheLaw of Nations, as quoted in Jeremy Rabkin, Why Sovereignty Matters, p. 27.

I. Introduction

What are the sovereign rights of nations in an interdependent world, and to what extent do

these rights stand in the way of achieving important international objectives? These two questions

rest at the heart of contemporary debate over the role and design of international institutions as well

as growing tension between globalization and the preservation of national sovereignty. But answers

are elusive. This is attributable in part to the fact that national sovereignty is a complex notion,

reflecting a number of different features. And it is attributable as well to the fact that nations interact

in increasingly complex and interdependent ways, making it difficult to draw clear distinctions

between international and domestic affairs.

In this paper, we provide answers to these two questions. We do so by first developing

formal definitions of national sovereignty that capture features of sovereignty emphasized in the

political science literature. We then utilize these definitions to describe the degree and nature of

national sovereignty possessed by governments in a benchmark world in which there exist no

international agreements of any kind. And with national sovereignty characterized in this benchmark

world, we then evaluate the extent to which national sovereignty is compromised by international

agreements with specific design features. In this way, we delineate the degree of tension between

national sovereignty and international objectives at the same time that we describe how that tension

can be minimized – and in principle at times even eliminated – through careful institutional design.

We focus our formal analysis on two prominent features of national sovereignty: the ability

of governments to exercise unilateral control over the issues that are important to them, and to

operate without outside influence in their internal affairs. The first feature indicates the extent to

which a government can dictate the outcomes over the things it cares about, and the second feature

indicates the extent that a government is free to determine its own affairs when other governments

are indifferent to its choices. Adopting a taxonomy described by Krasner (2001), we associate

interdependence sovereignty with the first feature and Westphalian sovereignty with the second.

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With our formal definitions of interdependence sovereignty and Westphalian sovereignty in hand,

we then turn to a characterization of the nature and degree of sovereignty that governments possess

in various environments.

We first consider a two-country two-good general equilibrium trading environment in which

each government makes choices over its import tariff and a set of domestic regulations. To identify

the degree of sovereignty that governments have in the absence of an international agreement, we

show that each government’s policy choices in the Nash equilibrium can be partitioned into a choice

of market access – the volume of imports it would accept at a particular foreign exporter (world)

price – given the other government’s policies, and then a choice of how best to use its available

policy instruments to deliver this level of market access. This partition is useful, because it enables

us to establish that governments typically possess neither interdependence sovereignty nor

Westphalian sovereignty in their market access choices in the absence of international agreements,

but that they enjoy complete sovereignty (i.e., both interdependence and Westphalian sovereignty)

in all other choices in this environment. Moreover, we show that this partition identifies the

maximal sovereign choice set over all possible partitions of the government’s policy choices. This

in turn establishes a benchmark set of sovereign choices in the absence of international agreements,

from which we evaluate the impact that international agreements may have on national sovereignty.

We begin this evaluation by considering an international trade agreement that specifies for

each government the negotiated level of its tariff and possibly also a subset of its regulations. Such

an agreement is natural to consider in this environment, because as we indicate the Nash equilibrium

policy choices of the two governments are inefficient from an international perspective, and so with

such an agreement the governments can potentially correct this inefficiency and thereby both enjoy

higher welfare. While an agreement of this form directly compromises national sovereignty over

the policy instruments that are directly negotiated, our first main result is that in general such an

agreement will also indirectly compromise national sovereignty over the policy instruments that

remain under unilateral control. Specifically, we show that the international trade agreement alters

each government’s choices over the policy instruments that remain in its unilateral control from the

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sovereign choices that it would have made absent the agreement given the same level of market

access. In this way, the sovereign choices of each government are compromised by an international

trade agreement of this form, even when many of the policy choices remain under unilateral control.

This result suggests a stark tradeoff between international efficiency – the attainment of which in

general requires an international trade agreement in this environment – and national sovereignty.

We next show, however, that this tradeoff is not inevitable. In particular, our second main

result is to establish that a market access agreement, under which each government agrees to provide

a specified level of market access to its trading partner but is otherwise free to choose its policies as

it sees fit, can in principle achieve international efficiency without compromising national

sovereignty. In effect, a market access agreement has the domestic and foreign governments making

joint determinations over the magnitudes for which they each lacked sovereignty in the Nash

equilibrium, but each government makes unilateral choices over the magnitudes for which it enjoyed

complete sovereignty in the Nash equilibrium. As the fundamental international inefficiency in this

environment amounts to insufficient market access, a market access agreement can in this way

address the source of the international inefficiency without compromising national sovereignty.

When viewed together, these first two results have potentially important implications for the

design of the World Trade Organization (WTO) and its predecessor, the General Agreement on

Tariffs and Trade (GATT). The GATT/WTO has from its inception been concerned most

fundamentally with market access commitments, and it has traditionally sought to anchor these

commitments with negotiations over border measures (e.g., tariffs). But increasingly the WTO is

being thought of as a potential forum for the negotiation of international commitments on a host of

non-border policies that are deemed to have important market access consequences, ranging from

labor standards to environmental regulations to competition policy. This possibility has fueled a

vigorous debate among WTO members about the wisdom of such changes in GATT/WTO practice.

Our first two results highlight the fundamental implications of this debate for the potential conflicts

between international efficiency and national sovereignty within the WTO. Specifically, as these

results indicate, the further the WTO moves away from basic market access commitments, the more

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it is likely to pose a (direct and indirect – and in principle, unnecessary) threat to the national

sovereignty of its member governments.

We next extend the two-country model to a three country setting. In particular, we introduce

a second foreign country, so that the domestic country now has two trading partners. This creates

the possibility that the domestic country might set discriminatory tariffs against each of its trading

partners, and allows us to consider the implications for national sovereignty of an international

agreement to abide by a non-discrimination rule, such as the MFN rule that GATT/WTO members

are required to submit to when they join. We ask: Is the domestic government’s sovereignty

compromised if it agrees to abide by a non-discrimination rule? Broadly speaking, we may think of

the answer to this question as indicating whether a government’s national sovereignty would be

compromised if it joined the GATT/WTO but made no market access commitments, and therefore

simply agreed to abide by the MFN principle of the GATT/WTO.

Our third main result is that abiding by the non-discrimination rule involves a direct

compromise of national sovereignty over tariff instruments, but entails no indirect compromise of

national sovereignty. Intuitively, discriminatory tariffs make possible certain market access choices

that would be impossible under MFN. But market access choices lack interdependence sovereignty

and Westphalian sovereignty even absent any international agreement. Therefore, for these choices,

the MFN restriction can not take away sovereignty that governments did not possess in the first

place. And given any market access choices that would be feasible under MFN, discriminatory

tariffs do not create any additional possibilities relative to MFN tariffs for delivering these market

access levels. Hence, for these decisions, which are a government’s sovereign choices, the MFN

restriction has no bearing. The only loss of national sovereignty is then reflected in the direct limit

on the tariff instruments imposed by the MFN requirement.

A natural question in our three-country setting concerns the sovereignty of “small” countries

who by definition cannot alter foreign exporter (world) prices when they alter their policies. As we

show, small countries differ from large countries in two ways. First, small countries suffer from an

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extreme lack of interdependence sovereignty in their market access choices, in that the foreign

exporter prices they face are completely determined by outside forces, and are thus completely

beyond their unilateral control. And second, small countries enjoy Westphalian sovereignty in their

market access choices: being small, all of a country’s trading partners are indifferent to its market

access choices, because these choices have no bearing on foreign exporter prices.

When we extend the three-country model to allow for the possibility that some (but not all)

countries are small, we find that a direct tradeoff between international efficiency and national

sovereignty may arise. In effect, if small countries are asked to make market access commitments,

their Westphalian sovereignty will be compromised. If this is to be avoided, then small countries

must be left unconstrained to choose their best-response policies in any international agreement.

This requirement, though, is inconsistent with international efficiency as long as discriminatory

tariffs are permitted. A non-discrimination rule is thus warranted on efficiency grounds, but entails

its own (direct) sacrifice of sovereignty over tariff instruments. Nevertheless, we show that the

degree to which sovereignty must be sacrificed to achieve international efficiency in this setting is

limited, in the sense that no further (indirect) compromise of sovereignty is required. In this way,

our three-country results suggest that a market access agreement coupled with a non-discrimination

rule can achieve international efficiency with minimal sacrifice of national sovereignty.

Finally, we extend our analysis from the case of international pecuniary externalities – which

drive the international inefficiencies that provide a reason for the existence of international trade

agreements in our models – to consider briefly the existence of important transborder non-pecuniary

externalities. An important distinction that arises here is that pecuniary externalities give rise to

inefficiency only if agents (in this case governments) wield market power and can therefore affect

prices (in this case world prices) with their actions, while with non-pecuniary externalities

inefficiency typically arises even when all agents are small and there is no market power affecting

decisions. As we argue, this distinction creates an inherent tradeoff between international efficiency

and (Westphalian) sovereignty in the presence of international non-pecuniary externalities when

some countries are small that, as we have described above, is not present in the case of international

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pecuniary externalities. This is because even small countries may have to make commitments

regarding an international non-pecuniary externality in order for the world to attain international

efficiency, and these countries will sacrifice their (Westphalian) sovereignty as a consequence.

On the basis of this final observation we argue that, when it comes to issues of national

sovereignty as they arise in the context of efforts to solve international problems, not all international

problems are alike. In particular, international problems that reflect inefficiencies that are

fundamentally driven by trade have a particular structure – they concern international pecuniary

externalities – which implies the absence of any inherent conflict between international efficiency

and national sovereignty. All other international problems – those that concern international non-

pecuniary externalities – pose a more direct efficiency/sovereignty tradeoff.

This paper builds on our earlier work. In particular, the basic two-country model with which

we begin in section II is developed in Bagwell and Staiger (2001). The three-country model

developed in section V extends the three-country model of Bagwell and Staiger (1999) to incorporate

domestic regulatory policies. In the present paper, however, we use these models to explore formally

the issue of national sovereignty.

The rest of the paper proceeds as follows. Section II describes the basic two-country model

and characterizes the Nash and efficient policies. Section III develops our formal definitions of

sovereignty, and characterizes the nature and degree of sovereignty in the Nash equilibrium. Section

IV considers how national sovereignty is affected under international trade agreements that adopt

alternative designs. Section V extends the modeling environment to a three-country setting, and

considers the implications of a non-discrimination rule and of the existence of small countries for

our sovereignty results. Section VI considers briefly the case of international non-pecuniary

externalities. Section VII concludes, while an Appendix contains more technical proofs.

II. Tariffs and Regulations in a Two-Country Trade Model

Our starting point is the two-country two-good competitive general equilibrium model

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adapted to allow for the possibility of both tariff and domestic regulatory policy choices as developed

in Bagwell and Staiger (2001). We sketch briefly the essentials of that model here.

II.1: The Basic Two-Country Trade Model

The home country exports good y to the foreign country in exchange for imports of good x.

The local relative price of good x to good y in the home (foreign) country is denoted by ( ),

where here and throughout “*” is used to denote foreign variables. The “world price” (i.e., relative

exporter price or terms of trade ) is denoted by , and international arbitrage links each country’s

local price to the world price in light of its tariff according to and

, where ( ) is one plus the ad valorem import tariff of the home

(foreign) country. In addition to its tariff, each country also imposes a vector of local regulations,

(with length ) for the home country and (with length ) for the foreign country, that may

impact local production and/or consumption decisions for given prices. Each country’s vector of

local regulations will therefore act as a vector of “shift” parameters in its import demand and export

supply functions, and we assume that these functions are differentiable in their respective regulation

levels.

Incorporating each country’s vector of regulations into its import demand and export supply

functions, we denote these functions for the home country by and ,

respectively, and for the foreign country by and , respectively. The

home and foreign budget constraints may then be written as

(1) ,

(2) .

The equilibrium world price, , is determined by the requirement of market clearing for

good x,

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(3) ,

where we have made explicit the dependence of the local prices on the tariffs and the world prices,

and market clearing for good y is then implied by (1), (2) and (3). We assume that the Metzler and

Lerner Paradoxes are ruled out, so that and .

Finally, we represent the objectives of the home and foreign governments with the general

functions and , respectively. These objective functions reflect an

important assumption: governments care about the regulatory (and tariff) choices of their trading

partners only because of the trade impacts of these choices (and therefore only because of the

impacts of these choices on the equilibrium world price ). As a consequence, the interdependence

across countries is contained entirely in the determination of , which is the only magnitude that

enters both the domestic and the foreign objective function. This feature reflects in turn a

simplifying assumption that we maintain for now, namely, that there are no international non-

pecuniary externalities. In a later section, we relax this assumption and consider briefly a setting in

which important transboundary non-pecuniary externalities may also exist.

We assume that, holding its regulations and its local price fixed, and provided that its

regulations and local price do not imply autarky, each government would prefer an improvement in

its terms of trade,

(4) for , and for .

According to (4), governments like transfers of revenue from their trading partners. Our central

analysis concerns the case in which trade takes place, and so (4) is relevant. However, we will report

one important special case in which no trade takes place, and so we develop the analogue to (4) that

applies in that circumstance. In the case of autarky, a change in the terms of trade holding its

regulations and local price fixed should be irrelevant to a government, since there is no trade volume

and continues to be no trade volume after the change, and so we assume as well that

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(4a) for , and for .

We leave government objectives otherwise unrestricted, and observe that these objectives are

consistent with a wide variety of models of government behavior (see Bagwell and Staiger, 1999).

II.2: Nash Policies

In a world without international agreements, we assume that the Nash Policy Game

characterizes the equilibrium policy choices of each government. In the Nash Policy Game, each

government sets its trade and domestic regulatory policies simultaneously to maximize its objective

function taking as given the policy choices of its trading partner. More specifically, the home

government chooses its best-response policies by solving

Program 1:

taking and as given, at the same time that the foreign government chooses its best-response

policies by solving

Program 1*:

taking and as given.

At an interior solution, the resulting Nash equilibrium choices are defined by the first-order

conditions:

(5) for ,

(6) ,

(7) for , and

(8)

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where, with the Metzler and Lerner paradoxes ruled out,

.

The home government reaction curves are defined by (5) and (6), while the foreign government

reaction curves are defined by (7) and (8), with the Nash equilibrium policy choices defined by the

joint solutions to these equations.

II.3: Efficient Policies

We next characterize efficient policy choices. Any efficient combination of policies will

achieve the maximal level of welfare for the home government given any fixed level of welfare for

the foreign government. The set of efficient policy combinations is defined as the set of solutions

to the first order conditions associated with this maximization problem, which with some

manipulation can be represented as:

(9) for ,

(10) for , and

(11) ,

where and .

Here we simply observe that one efficient solution is what we have previously (Bagwell and

Staiger, 2001) called the politically optimal solution, defined by

(12) for ; and for .

III. National Sovereignty without International Agreements

We are now ready to consider formally the issue of national sovereignty. To begin, we need

to define what we mean by national sovereignty.

1Even here it can be argued that national sovereignty is preserved provided that the ultimate decision to leave theagreement remains in the hands of a national government. While acknowledging that such ambiguities exist in anydiscussion of national sovereignty, we nevertheless abstract from a number of these to focus analytically on what webelieve are the most important features.

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III.1: Sovereignty Defined

An obvious feature of sovereignty is the possession of the sole decision-making authority in

determining one’s policies. If the level of a policy instrument is directly negotiated between or

among governments, it seems reasonable to conclude that national sovereignty over that policy

instrument has been lost, at least as long as the agreement is in force.1 A definition of sovereignty

should reflect this feature.

But beyond this, it also seems that national sovereignty over a set of policy instruments might

be threatened indirectly even when direct authority over the setting of those policy instruments

remains in the hands of a national government. This threat is emphasized by Rabkin (1998), who

observes:“If sovereignty is defined as the ultimate authority to reject outside control, then all talk of threats to Americansovereignty may appear quite absurd, especially while America remains the world’s only superpower. But that is...anextremely crude way of viewing the question of sovereignty.

“The real threat is not that the United States will be forced to act against the determined resolve of the Americanpolitical system. Rather, the threat is that international commitments will distort or derange the normal workings of ourown system, leaving it less able to resolve policy disputes in ways acceptable to the American people.” Rabkin (1998,p. 34).

For example, as a result of an international agreement, a government might be compelled to

abide by a set of rules when setting its policies, even though the government may retain control over

its own policy choices within the limits dictated by these rules. The MFN rule by which

governments agree to abide when they join the GATT/WTO is an example of this kind of restraint

in the context of the “unbound” tariff choices of a member government. More subtle is the

possibility that international agreements over certain policies could have the effect of eroding the

sovereignty of national choices over other “domestic” policies. The notion that GATT/WTO tariff

commitments may be fueling a “race to the bottom” in domestic regulatory policies reflects this kind

of possibility.

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Moreover, even absent international agreements, a government may feel constrained by the

unilateral policy choices of other governments. In this regard, a government might feel that the

choices it has available to it for imposing costly regulations on its export industries are constrained

by the unilateral policy choices of governments in other countries whose export industries compete

for world markets. More generally, governments may consider it to be a loss of national sovereignty

when the “discipline” imposed by international markets constrains their options. This point is often

made in the context of international capital flows, but the logic can be equally applied to

comparative-advantage based changes in the location of global production that occur even when

factors of production are themselves internationally immobile. In effect, governments use policies

to induce outcomes over things they care about, and the policy choices of one government may

constrain the possible outcomes that another government’s policy choices can induce, even if there

is no international agreement between the two governments.

As this discussion indicates, defining sovereignty is not a simple task. In fact, Krasner (2001)

identifies four distinct ways in which the term “sovereignty” has been commonly used in the

international political science literature. Krasner refers to these as domestic sovereignty,

international legal sovereignty, interdependence sovereignty, and Westphalian sovereignty (p. 3).

Domestic sovereignty refers to the organization and effectiveness of political authority within the

state. International legal sovereignty refers to the mutual recognition of states. Interdependence

sovereignty refers to the scope of activities over which states can effectively exercise unilateral

control. And Westphalian sovereignty reflects as its central premise the rule of nonintervention in

the internal affairs of other states.

In principle, international agreements could have important implications for any of these four

notions of sovereignty. Nevertheless, we will focus our analytical work on the implications of

international agreements for interdependence sovereignty and Westphalian sovereignty, as these

notions seem most closely related to the issues at the heart of our discussion above.

To try to capture these features of national sovereignty, we propose the following definitions.

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In essence, we associate with interdependence sovereignty the notion of unilateral control, and with

Westphalian sovereignty the notion of internal affairs:

Definition: A government exercises unilateral control in a choice problem provided that its payoffin that choice problem is unaffected by the choices of other governments. A government hasinterdependence sovereignty in any choice problem within which it exercises unilateral control. Agovernment has perfect interdependence sovereignty if it has interdependence sovereignty in all itschoice problems.

Definition: A government’s choice problem concerns its internal affairs provided that all other

governments are indifferent to the outcome of that choice problem. A government has Westphalian

sovereignty over any choice problem that concerns its internal affairs. A government has perfect

Westphalian sovereignty if it has Westphalian sovereignty in all its choice problems.

Definition: A government has sovereignty over any choice problem for which it has bothinterdependence and Westphalian sovereignty. A government has absolute sovereignty if it hassovereignty in all its choice problems.

In the remainder of the paper, we will explore the nature of national sovereignty in various

international settings using the definitions above. In each case, we evaluate the degree of sovereignty

according to a local criterion, by asking what degree of sovereignty is present for small policy

changes around an equilibrium.

III.2: Sovereignty in the Absence of International Agreements

With sovereignty defined, we next characterize the nature and degree of sovereignty

possessed by each government in the Nash Policy Game. This provides an important benchmark,

because the impact of an international agreement on a nation’s sovereignty can only be assessed once

the nature and degree of sovereignty absent the agreement is understood. The sovereignty possessed

by a government in the Nash Policy Game thus provides a natural baseline from which to gauge the

impact of any international agreement.

Our approach is to propose a particular partition of a government’s best-response choice

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problem into an equivalent problem in which two sub-problems are solved sequentially, and then

to show that the government enjoys sovereignty over the choices it faces in the first-step sub-

problem, but that it (generally) does not have sovereignty over the choices it faces in the second-step

sub-problem. Our argument is then completed by establishing that the second-step choices that the

government faces in this particular partition are also necessary in any other partition that produces

sovereign choices in the associated first-step sub-problem. With this established, we may conclude

that our proposed partition identifies the maximal sovereign choice set for each government in the

Nash Policy Game. As a consequence of this argument, we thus define a government’s sovereign

choices as the choices it makes in the first-step sub-problem of our chosen partition.

We develop this partition from the perspective of the domestic government (an analogous

development holds for the foreign government). To this end, recall the best-response policy choice

problem of the domestic government, defined by Program 1 in the previous section. Using the

market-clearing condition (3) that determines , Program 1 (which takes and as given) can

be equivalently written as

s.t. ,

which is in turn equivalent to

s.t.

for any M.

Consider now the partition of this program into the alternative 2-step program:

Program 1': Step 1. Fix , and

s.t. .

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Step 2.

s.t. ,

where and are the solutions from Step 1 and is the Step-1 Lagrangean. For

future reference, we denote by the Lagrangean associated with the Step-2 sub-problem.

The 2-step partition defined in Program 1' may be interpreted as follows. Following Bagwell

and Staiger (2001), we define the level of market access as the volume of imports a country would

accept at a particular world price. Accordingly, the Step-1 choice problem in Program 1' describes

the domestic government’s choice of tariff and regulatory policies among the feasible domestic

policy combinations defined by the domestic market-access constraint for any given level of

domestic market access, i.e., among the feasible domestic policy combinations defined by

for any . The Step-2 choice problem in Program 1' then

describes the domestic government’s choice of a particular domestic market access level among the

feasible domestic market access levels defined by the foreign export supply curve for any given level

of foreign policies and the requirement of market clearing, i.e., among the feasible domestic market

access levels defined by the constraint for any .

To establish that Program 1 and Program 1' are equivalent ways of expressing the domestic

government’s best-response policy choice problem, we first record the first-order conditions that

define the solutions to the Step-1 and Step-2 sub-problems of Program 1'. Using the Envelope

Theorem, and with denoting the Lagrange multiplier associated with and denoting the

Lagrange multiplier associated with , the first-order conditions associated with the domestic

government’s Step-1 sub-program are

(13) for , and

(14) ,

2Of course, different levels of and may lead to different choices of and , but the point is that thesechoices are made by the domestic government in Step 2, and therefore and are taken as fixed in Step 1.

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while the first-order conditions associated with the domestic government’s Step-2 sub-program are

then

(15) , and

(16) .

We may now state:

Lemma 1: Program 1 and Program 1' are equivalent ways of characterizing the domestic

government’s best-response policies for any and .

Proof: See Appendix.

We prove Lemma 1 by establishing that the first-order conditions associated with Program 1', (13)-

(16), are equivalent to the first-order conditions associated with Program 1, (5)-(6).

In light of Lemma 1, we next characterize the degree of sovereignty that the domestic

government enjoys in the Nash Policy Game when sovereignty is evaluated using the particular

partition of the domestic government’s best-response choice problem described by Program 1'.

While a completely analogous result to Lemma 1 may be stated for the foreign government, we

continue to focus on the domestic government, and begin with its Step-1 choices.

In Step 1 of Program 1', the levels of and are taken as fixed, because they are

determined by the domestic government in its Step-2 sub-problem. Hence, the domestic government

exercises unilateral control in its Step 1 choice problem since, with and given, its payoff in

that choice problem is unaffected by the choices of the foreign government.2 Accordingly, the

domestic government has interdependence sovereignty in its Step-1 choice problem. Moreover, the

3That is, for given and , the foreign government is indifferent over combinations of and that deliverthe same and hence (by the requirement of market clearing given by ), asindicated by its implied welfare level .

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Step-1 choice problem of the domestic government concerns its internal affairs since, with and

determined in its Step-2 sub-problem, the foreign government is indifferent to the outcome of the

domestic government’s Step-1 choice problem.3 Accordingly, we may conclude that the domestic

government has Westphalian sovereignty in its Step-1 choice problem as well.

Exactly analogous observations hold for the foreign government’s Step-1 choice problem.

Let us denote by and the solutions from the foreign government’s analogous

Step-1 problem. Finally, we denote by the (length ) vector of domestic policy

instruments chosen by the domestic government in its Step-1 problem, and similarly we denote by

the (length ) vector of foreign policy instruments chosen by the foreign

government in its Step-1 problem. We may now state:

Proposition 1: When evaluated using the partition described in Program 1', each government’schoice of how best to use its available policy instruments to deliver any level of market access (i.e,

the function for the domestic government and the function for the foreign

government) is sovereign in the Nash Policy Game.

Consider next the domestic government’s Step-2 choices. The foreign government’s policy

choices influence the domestic government’s payoff in this choice problem through the constraint

in the domestic government’s Step-2 program. As a consequence, the domestic government

exercises unilateral control in its Step-1 choice problem if and only if the multiplier on this

constraint, , is zero. In addition, the foreign government is indifferent to the outcome of the

domestic government’s Step-1 choice problem – and therefore this choice problem concerns the

domestic government’s internal affairs – if and only if the foreign government is indifferent to

changes in the world price (i.e., ). In general, neither of these conditions will hold in our

4We consider how these statements must be modified to accommodate the possibility of “small” countries insection V, where we develop a many country model.

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two-country model, and so in general each government will enjoy neither interdependence

sovereignty nor Westphalian sovereignty in its Step-2 choice problem.4

As a general matter, then, Proposition 1 provides the full characterization of the degree of

sovereignty enjoyed by governments in the Nash Policy Game when evaluated using the partition

described in Program 1'. However, there is one special case where governments do enjoy some

sovereignty in their Step-2 choices, and in this case it turns out that they enjoy both interdependence

and Westphalian sovereignty in their Step-2 choices. In light of Proposition 1, we characterize this

special case as follows:

Proposition 2: When evaluated using the partition described in Program 1', governments enjoyabsolute sovereignty in the Nash Policy Game if and only if the politically optimal choices of tariffsand standards imply autarky.

Proof: To prove this proposition, we need only (in light of Proposition 1) establish that the Step-2

choice problem of each government is sovereign if and only if the politically optimal choices of

tariffs and standards imply autarky. We consider the home government, and recall that sovereignty

in its Step-2 choice problem arises if and only if (i) , and (ii) . Using (13)-(16), we may

derive the following three expressions for :

(17a) for ;

(17b) ; and

(17c) .

By (17a)-(17c), (12) and (4a), if and only if the politically optimal choices of tariffs and

5This Corollary is not stated as an if-and-only-if statement, because efficiency of the Nash Policy Game does notgenerally imply absolute sovereignty when evaluated using the partition described in Program 1', as consideration ofthe case of a world of “small” countries confirms (see also note 4).

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standards imply autarky, which by (4a) implies as well that . An analogous argument applies

to the foreign government. QED

As politically optimal policy choices are efficient, an immediate implication of Proposition

2 is the following:

Corollary: When evaluated using the partition described in Program 1', policy choices in the NashPolicy Game are absolutely sovereign only if they are also efficient.5

Hence, as Proposition 2 and its Corollary indicate, when evaluated using the partition described in

Program 1', absolute sovereignty is achievable in the absence of international agreements only when

(i) countries are in absolute isolation, and (ii) this isolation is internationally efficient, and so there

is no reason for the existence of international agreements.

Together, Propositions 1 and 2 imply that, when evaluated using the partition described in

Program 1', the sovereign choices of each government in the Nash Policy Game (outside the

absolute-isolation benchmark) are described by the respective functions and .

In effect, in the Nash Policy Game each government maintains sovereignty over all choices other

than its market access choices: but governments enjoy neither Westphalian nor interdependence

sovereignty over their market access choices, despite the fact that there is no international agreement

in the Nash Policy Game. Of course, this characterization of sovereignty depends upon the particular

(and potentially arbitrary) partition described in Program 1'. However, we next suggest that this

partition provides a sensible basis from which to characterize sovereignty in the Nash Policy Game,

because the constraints imposed in Step 1 under this partition are a subset of the constraints imposed

in Step 1 under any other partition that yields sovereign Step-1 choices. As a consequence, the

partition described in Program 1' may be said to identify the maximal sovereign choice set for each

government in the Nash Policy Game.

20

More specifically, we now turn to the final step of our argument, and establish that the

second-step choices that the government faces in the partition defined in Program 1' are also

necessary in any other partition that produces sovereign choices in the associated first-step sub-

problem. The only exception to this statement arises in the absolute-isolation benchmark case

identified in Proposition 2, where governments enjoy absolute sovereignty in the Nash Policy Game

when evaluated using the partition described in Program 1': in that case, any partition of the

government’s best-response choice problem will yield the same characterization of sovereignty. We

record this finding in:

Lemma 2: If a partition of the domestic (foreign) government’s best-response choice problem

contains a sub-problem within which the domestic (foreign) government’s choices are sovereign,

then the level of domestic (foreign) market access must be determined by domestic (foreign) choices

outside of this sub-problem, unless governments enjoy absolute sovereignty in the Nash Policy

Game.

Proof: Consider the domestic government. Suppose that, under a certain partition of the

government’s best-response choice problem, there exists a sub-problem within which the domestic

government’s choices are sovereign. If the level of domestic market access is not determined by the

domestic government’s choices outside of this sub-problem, then it must be determined by the

domestic government’s choices in this sub-problem. In this sub-problem, then, the domestic

government must (i) make choices which determine the market-clearing world price , and (ii) face

the constraint (possibly among multiple constraints) on feasible domestic market access levels

defined by the foreign export supply curve and the requirement of market clearing, i.e.,

. But unless governments enjoy absolute sovereignty in the Nash

Policy Game, Westphalian sovereignty is precluded by (i), while interdependence sovereignty is

precluded by (ii), contradicting the original supposition that the domestic government’s choices are

sovereign in this sub-problem. Therefore, the level of domestic market access must be determined

by choices outside of this sub-problem, unless governments enjoy absolute sovereignty in the Nash

Policy Game. QED

21

According to Lemma 2, as long as attention is restricted to settings in which absolute

isolation is not efficient – a restriction we maintain from here on – then the partition of the domestic

government’s best-response policy choices described in Program 1' identifies the maximal sovereign

choice set over all possible partitions of the domestic government’s best-response policy choices:

as described by the choice function , the choices that the domestic government makes over

its maximal sovereign choice set concern everything that it cares about except the level of market

access it affords to the foreign country. Lemma 2 implies that any other sovereign choice set

associated with any other partition of the government’s best-response policy choices must also

exclude market access (and if different from the maximal sovereign choice set described by Program

1', must exclude other choices as well). With analogous observations for the foreign government,

we may therefore state:

Proposition 3: The choice functions and describe, respectively, the choices

that the domestic and foreign government make over their maximal sovereign choice sets in the Nash

Policy Game.

Armed with Proposition 3, we now associate the domestic and foreign government’s

sovereign choices with the respective choice functions and . In the following

sections, we use these functions to evaluate the erosion of national sovereignty that may occur once

governments negotiate international agreements.

IV. National Sovereignty and International Trade Agreements

In this section we explore the ways in which international trade agreements may erode

national sovereignty. As discussed in section III.1, international agreements may encroach on

national sovereignty both directly and indirectly. We will say that a government’s sovereignty over

a policy instrument is directly compromised by an international agreement whenever limits on that

policy instrument are directly negotiated between or among governments. We will say that a

government’s sovereignty is indirectly compromised by an international agreement whenever there

exists a policy instrument for which the government’s sovereignty is not directly compromised by

22

the international agreement but for which the government’s unilateral choice differs from itssovereign choice (i.e., differs from the corresponding element of – for the domestic

government – or – for the foreign government) evaluated at the level of market accessdelivered under the agreement.

Consider first an international trade agreement that specifies the tariff levels to be applied

by each government and also possibly the regulatory levels for a subset of domestic regulations and

a subset of foreign regulations. Let the domestic regulations that are not determined directly by the

international agreement be contained in the set , and let the foreign regulations that are not

determined directly by the international agreement be contained in the set . If the international

trade agreement concerns only tariff levels, then the set contains the entire vector of domestic

regulations and the set contains the entire vector of foreign regulations . Otherwise, these

sets contain only a subset of the elements of the respective regulatory vectors.

We may now state:

Proposition 4: The domestic (foreign) government’s sovereignty is indirectly compromised by an

international trade agreement that specifies levels for its tariff and a subset of its regulations if and

only if (i) the levels of its policies specified in the agreement differ from its unilateral best-response

levels, and (ii) ( ) is non-empty.

Proof: We adopt the perspective of the domestic government. If is empty, then the international

trade agreement has left no domestic instruments under the unilateral control of the domestic

government, and therefore its sovereignty cannot be indirectly compromised. If instead is non-

empty, then let be the vector of domestic regulatory choices under the domestic government’s

control, and let be the domestic tariff level and be the vector of domestic regulations specified

by the international trade agreement. Given any foreign policies and , the domestic

government’s unilateral best-response choice of must solve the program:

23

Program 2:

taking and as given. The first-order conditions for Program 2 are given by (5) for the

domestic regulatory choices contained in . Now consider the partition of this program into the

alternative 2-step program:

Program 2': Step 1: Fix , and

s.t. .

Step 2:

s.t. ,

where is the solution from Step 1 and is the Step-1 Lagrangean. Arguments identical

to those in the proof of Lemma 1establish that Program 2 and Program 2' are equivalent ways of

characterizing the domestic government’s unilateral best-response choice of . Hence, to complete

the proof we need only observe that the elements of are equal to the corresponding

elements of when both functions are evaluated at the market access level delivered by the

domestic government under the international trade agreement, if and only if and are each set at

their unilateral best-response levels: when this is the case, the Step-2 choice of and will

correspond to the unilateral best-response choices, and the elements of are equal to the

corresponding elements of when both functions are evaluated at this market access level;

when this is not the case, the Step-2 choice of and will differ from the unilateral best-

response choices, and the elements of must then differ from the corresponding elements

of when both functions are evaluated at this market access level. An analogous argument

applies to the foreign government. QED

According to Proposition 4, any international trade agreement that moves a government away

24

from its unilateral best-response policies by specifying permissible levels for a subset of that

government’s policies will indirectly compromise that government’s sovereignty over the

instruments that remain under its unilateral control. Combined with the direct compromise of

sovereignty that comes from directly negotiating policy levels, this seems to suggest a basic tradeoff

that governments must confront between international efficiency – which in general cannot be

achieved in the absence of an international trade agreement – and national sovereignty. However,

the existence of this tradeoff is not inevitable. As we next show, an international agreement can be

designed in such a way as to avoid the need to sacrifice national sovereignty in pursuit of

international efficiency.

To establish this, we will say that a government’s sovereignty is preserved by an international

agreement if its sovereignty is neither directly nor indirectly compromised. Consider, then, the

following market access agreement. Under a market access agreement, the domestic government

agrees to abide by a specified domestic market access constraint defined by a level of domestic

import volume and world price level , , but the domestic government is

otherwise free to choose its tariff and domestic regulations . Similarly, the foreign government

agrees to abide by a specified foreign market access constraint defined by a level of foreign import

volume and world price level , , but the foreign government is

otherwise free to choose its tariff and foreign regulations . Notice that a market access

agreement has the domestic and foreign governments making joint determinations over the

magnitudes for which, according to Proposition 3, they each lack sovereignty in the Nash Policy

Game (namely, the Step-2 choices of each government), but each government continues to make

unilateral choices in a market access agreement over the magnitudes for which it enjoys sovereignty

in the Nash Policy Game according to Proposition 3 (namely, the Step-1 choices of each government

as embodied in and ).

We may now state:

Proposition 5: Market access agreements preserve the sovereignty of each government.

25

Proof: The proof is immediate, since (i) neither government’s sovereignty is directly compromised,

and (ii) given its domestic market access constraint the domestic government then chooses ,

while given its foreign market access constraint the foreign government then chooses ,

and so neither government’s sovereignty is indirectly compromised. QED

We have established in Bagwell and Staiger (2001, Proposition 1) that the nature of the

international inefficiency in the Nash equilibrium of this model is an insufficient level of market

access, and it is therefore direct that a market access agreement can achieve international efficiency

by expanding market access to an efficient level. As a consequence, we may also state the

following:

Corollary: Market access agreements involve no tradeoff between international efficiency andnational sovereignty.

Propositions 4, 5 and the Corollary have potentially important implications for the design of

international trade agreements. The GATT/WTO has from its inception been concerned most

fundamentally with market access commitments. While the GATT traditionally sought to anchor

these commitments with negotiations over border measures (e.g., tariffs), the negotiated

commitments were consistently interpreted as concerning access, not the particular level of a given

policy instrument (see, for example, Bagwell and Staiger, 2001). Increasingly, however, the WTO

is seen as a potential forum for the negotiation of international commitments on a host of non-border

policies that are deemed to have important market access consequences, ranging from labor

standards to environmental regulations to competition policy. Our results highlight the fundamental

implications of this development for the potential conflicts between international efficiency and

national sovereignty within the WTO. Specifically, as these results indicate, the further the WTO

moves away from basic market access commitments, the more it is likely to pose a (direct and

indirect – and in principle, potentially unnecessary) threat to the national sovereignty of its member

governments.

6The other important non-discrimination rule in the GATT/WTO is that of “national treatment,” which applies tonon-border measures. In our formal model, the MFN rule would apply to tariffs, while the national treatment rulewould apply to regulations. We focus here on the implications of the MFN rule for national sovereignty, butanalogous findings could be formalized with regard to national treatment.

26

V. National Sovereignty and Non-discrimination

We now extend the two-country model with standards to a three-country setting. In

particular, we introduce a second foreign country, so that the domestic country now has two trading

partners. This creates the possibility that the domestic country might set discriminatory tariffs

against each of its trading partners, and allows us to consider the implications for national

sovereignty of an international agreement to abide by a non-discrimination rule, such as the MFN

rule to which governments must adhere when they join the GATT/WTO.6 The three-country model

is based on the multi-country model in Bagwell and Staiger (1999), adapted to allow for the

possibility of both tariff and domestic standards choices.

V.1: The Three Country Trade Model

The home country exports good y to foreign countries 1 and 2 in exchange for imports of

good x from each of them. For simplicity, we do not allow trade between the two foreign countries,

and so only the home country has the opportunity to set discriminatory tariffs across its trading

partners. The local relative price of good x to good y in the home country (foreign country j) is

denoted by ( , j=1,2). The “world price” (i.e., relative exporter price) for trade between the

home country and foreign country j is denoted by , and international arbitrage links each

country’s local price to the relevant world price in light of its tariff according to ,

and for j=1,2, where ( ) is one plus the ad valorem import tariff

that the home country (foreign country j) applies to the imports from foreign country j (the home

country). This implies in turn that world prices are linked across bilateral relationships:

(18) .

As in the two-country model above, in addition to its tariff, each country also imposes a vector of

local regulations, (with length ) for the home country and (with length ) for foreign

27

country j, that may impact local production and/or consumption decisions for given prices. Each

country’s vector of local regulations will therefore act as a vector of “shift” parameters in its import

demand and export supply functions, and as before we assume that these functions are differentiable

in their respective regulation levels.

Incorporating each country’s vector of regulations into its import demand and export supply

functions, we denote these functions for the home country by and , respectively,

and for foreign country j by and , respectively, where is the

home-country’s multilateral terms of trade, and is defined by

with

for j=1,2.

The home and foreign budget constraints may then be written as

(19) , and

(20) for j=1,2.

The pair of equilibrium world prices, for j=1,2, are then determined by

the linkage condition (18) together with the requirement of market clearing for good x,

(21) ,

with market clearing for good y then implied by (19) and (20). As before, we assume that the

Metzler- and Lerner- Paradox type outcomes are ruled out, so that and

for j=1,2.

Finally, in analogy with our two-country model, we represent the objectives of the home and

28

foreign government j=1,2 with the general functions and , respectively.

As before, we assume that, holding its regulations and its local price fixed, and provided that its

regulations and local price do not imply autarky, each government would prefer an improvement in

its terms of trade,

(22) for , and for .

We leave government objectives otherwise unrestricted.

V.2: Nash Policies

In a three-country world without international agreements, we assume that the Multilateral

Nash Policy Game characterizes the equilibrium policy choices of each government. In the

Multilateral Nash Policy Game, each government sets its trade and domestic regulatory policies

simultaneously to maximize its objective function taking as given the policy choices of all other

governments. More specifically, the home government chooses its best-response policies by solving

Program 3:

taking and for j=1,2 as given, at the same time that foreign government j , for j=1,2, chooses

its best-response policies by solving

Program :

taking as given , and and for k=1,2 and .

At an interior solution, the resulting Nash equilibrium choices are defined by the first-order

conditions:

(23) for ,

(24) , for ,

29

(25) for , and

(26) for ,

where, with the Metzler and Lerner paradoxes ruled out,

.

We observe that, by the linkage condition (18), , and so (23) may be

equivalently evaluated for either j=1,2. The home government reaction curves are defined by (23)

and (24), while foreign government j’s reaction curves are defined by (25) and (26), with the Nash

equilibrium policy choices defined by the joint solutions to these equations.

V.3: Efficient Policies

We characterize efficient policy choices in the Appendix (see the proof of Proposition 6).

Here we simply define the politically optimal tariffs and regulations:

(27) for ; for ; and for .

In the Appendix we prove:

Proposition 6: Politically optimal tariffs and regulations are efficient if and only if the tariffsconform to MFN. Moreover, if any country sets its politically optimal policies, then efficiencyrequires that all countries set their politically optimal policies and abide by MFN.

Proof: See Appendix.

V.4: Sovereignty in the Absence of International Agreements

As with our two-country model, we next observe that the Nash policy choices defined by the

simultaneous solutions to Program 3 and Program may be written in an equivalent form in which

each government’s program is partitioned into a 2-step choice problem. Following our two-country

presentation, we develop this partition from the perspective of the domestic government.

30

To this end, recall the best-response policy choice problem of the domestic government

defined by Program 3. In analogy with the two-country model, in which the best-response policy

choice problem contained in Program 1 was transformed into Program 1' by first introducing

as a choice variable and adding the market-clearing condition (3) as a constraint, we now transform

Program 3 by first introducing , and as choice variables and adding the appropriate

constraints. The three new constraints are the linkage condition (18), the market-clearing condition

(21), and the definition of in terms of the foreign regulatory choices and the foreign local and

world prices. However, rather than introduce the linkage condition explicitly, it is convenient to

instead use this condition to eliminate as an independent choice variable in the domestic

government’s best-response problem. And rather than introduce explicitly the definition of , it is

convenient instead to use this definition to eliminate as an independent choice variable in the

domestic government’s best-response problem. Utilizing (18) and the definition of in this way,

and using to denote , Program 3 (which takes

and for j=1,2 as given) can be equivalently written as

s.t. ,

which is in turn equivalent to

s.t.

for any . Observe that, taking and for j=1,2 as given, is determined once and

are chosen.

Consider now the partition of this program into the alternative 2-step program:

31

Program 3': Step 1. Fix , and

s.t. .

Step 2.

s.t. ,

where and are the solutions from Step 1 and is the Step-1 Lagrangean.

For future reference, we denote by the Lagrangean associated with the Step-2 sub-problem.

Using the Envelope theorem, and with denoting the Lagrange multiplier associated with

and denoting the Lagrange multiplier associated with , the first-order conditions associated with

the domestic government’s Step-1 program are then

(28) for , and

(29) ,

while the first-order conditions associated with the domestic government’s Step-2 program are

(30) ,

(31) ,

(32) .

We may now state:

Lemma 3: Program 3 and Program 3' are equivalent ways of characterizing the domestic

government’s best-response policies for any , , and .

32

Proof: See Appendix.

In exact analogy with our two-country model, we may by Lemma 3 utilize the 2-step

representation of the domestic government’s best-response policies developed just above to

characterize the nature and degree of national sovereignty enjoyed by the domestic government in

the Multilateral Nash Policy Game. As in the two-country setting, an examination of the domestic

government’s Step-1 choice problem indicates that it enjoys (both interdependence and Westphalian)

sovereignty over these choices. Similarly, an examination of the domestic government’s Step-2

choice problem indicates that, except for the case of absolute isolation, the domestic government

enjoys neither interdependence sovereignty nor Westphalian sovereignty over these choices.

Finally, it may be established as in the two-country setting that the partition embodied in

Program 3' identifies the maximal sovereign choice set over all partitions of the domestic

government’s best-response policy choices. Denoting by the (length ) vector of

policy instruments chosen by the domestic government in its Step-1 problem (namely,

and ), we may thus conclude that, as described by the choice function ,

the choices that the domestic government makes over its maximal sovereign choice set concern

everything that it cares about except the level of market access it affords to each of the two foreign

countries (as defined by the volume of imports it would accept at a particular pair of bilateral world

prices). Hence, as in the two-country setting, we associate in our three-country model the domestic

government’s sovereign choices with the domestic government’s choice function .

Observing that foreign countries 1 and 2 are exactly analogous to the foreign country in the two-

country model, we may also denote the sovereign choice function of foreign government j for j=1,2,

by .

V.5: Sovereignty and Non-discrimination

We may now ask the central question of this section: Is the domestic government’s

sovereignty compromised if it agrees to abide by a non-discrimination rule? Broadly speaking, we

33

may think of the answer to this question as indicating whether a government’s national sovereignty

would be compromised if it joined the GATT/WTO but made no market access commitments, and

therefore simply agreed to abide by the MFN principle of the GATT/WTO. We answer this question

in two parts.

First, above we have defined a government’s sovereignty over a policy instrument to be

directly compromised by an international agreement whenever limits on that policy instrument are

directly negotiated between or among governments. Clearly the non-discrimination rule is a

negotiated limit on the domestic government’s instruments, of the form . Hence, we may

conclude that the domestic government’s sovereignty over its tariff instruments is directly

compromised when it accepts a non-discrimination rule.

But the more interesting question is whether the domestic government’s sovereignty is also

indirectly compromised, and this is the focus of the second part of our answer. To provide an

answer, we now observe using the linkage condition (18) that the MFN rule restricts the feasible

Step-2 choices of and to those that satisfy , but leaves the Step-1 choices of the

domestic government unrestricted given its Step-2 choices. Accordingly, we may

conclude that the domestic government’s sovereignty is not compromised indirectly when it agrees

to abide by the non-discrimination rule. We may therefore state:

Proposition 7: Abiding by the non-discrimination rule involves a direct compromise of nationalsovereignty over tariff instruments, but entails no indirect compromise of national sovereignty.

Proposition 7 reflects the following intuition. Discriminatory tariffs make possible certain

market access choices that would be impossible under MFN. But market access (Step-2) choices

lack interdependence sovereignty and Westphalian sovereignty in the Multilateral Nash Policy

Game. Therefore, for these choices, the MFN restriction can not take away sovereignty that

governments did not possess in the first place. And given any market access choices that would be

feasible under MFN, discriminatory tariffs do not create any additional possibilities relative to MFN

7If all countries are small, then it can be shown that the Multilateral Nash Policy Game yields policy choices thatare efficient from an international perspective, and so there would be no reason for an international agreement toexist in this case (see Bagwell and Staiger, 1999, 2001).

34

tariffs for delivering these market access levels. This feature is reflected in the fact that the Step-1

choices of Program 3' may be expressed as choices over domestic regulations and a single tariff

. Hence, for these decisions, which are the (Step-1) decisions over which governments enjoy

sovereignty in the Multilateral Nash Policy Game, the MFN restriction has no bearing. The only loss

of national sovereignty is then reflected in the direct limit on the tariff instruments imposed by the

MFN requirement (i.e., ).

Thus far we have maintained an assumption in the three-country model (consistent with our

two-country model) that all countries are “large,” in the sense that each has an impact on world

prices when it alters its policies. In the next subsection, we consider the possibility that some

countries might be “small,” and so do not alter world prices when they alter their policies.7

However, before turning to a setting in which some countries are large and some are small, we record

a final result for the world in which all countries are large.

In light of Propositions 5 and 7, we may state:

Proposition 8: If all countries are “large,” market access agreements that require governments to

abide by the non-discrimination rule: (i) directly compromise national sovereignty over tariff

instruments; but (ii) involve no further sacrifice of national sovereignty.

V.6: The Sovereignty of Small Countries

We now treat foreign country 2 as a foreign region which is composed of a continuum of

identical “small” foreign countries, none of which individually has any impact on world markets.

We observe that, in light of the assumed symmetry of countries within region 2, the domestic

government will not discriminate across foreign countries within region 2 in a symmetric Nash

equilibrium (i.e., the domestic government’s best-response tariffs will continue to consist of a tariff

35

against imports from foreign country 1 and a tariff against imports from all foreign countries

residing in region 2).

It can immediately be seen that Program 3' continues to provide a valid 2-step representation

of the domestic government’s best-response choices of , and given any and

imposed by foreign country 1 and any and imposed symmetrically by each foreign country

in region 2. This means in turn that, in the (symmetric) equilibrium of the Multilateral Nash Policy

Game, the domestic government continues to enjoy sovereignty over its Step-1 choices, and it

continues to lack both interdependence sovereignty and Westphalian sovereignty in its Step-2

choices, when foreign region 2 is interpreted as being composed of many small countries. An

analogous statement can be shown to apply to foreign country 1: the government of foreign country

1 continues to enjoy sovereignty over its Step-1 choices , and it continues to lack both

interdependence sovereignty and Westphalian sovereignty in its Step-2 choices , when

foreign region 2 is interpreted as being composed of many small countries.

However, an important difference in sovereignty arises for the small foreign countries of

region 2. A representative foreign government c in region 2, being small, takes the market clearing

world price for trade between the domestic country and region 2, , as given and fixed at

, where and represent the (symmetric) policy levels of all

other small countries in foreign region 2. As a general matter, world prices are taken as fixed (at the

levels implied by Step-2 choices) in the Step-1 choice problem, and so the Step-1 choice problem

for this representative region-2 government is not altered from before. Specifically, letting “c”

denote variables associated with a representative region-2 government, its Step-1 program is:

Step 1. Fix , and

s.t. .

But with denoting the Lagrangean associated with c’s Step-1 program, and with

36

( ) denoting the choices that solve c’s Step-1 program, the Step-2 choice

problem for this representative region-2 government is now:

Step 2.

s.t. .

Evidently, while the Step-2 choices of the government of a representative small country in

region 2 lack interdependence sovereignty in the extreme – the constraint imposed by the policies

of all other countries now completely dictates the relevant world price for the government of

country c – these Step-2 choices now do reflect Westphalian sovereignty: with the government of

country c unable to alter with its Step-2 choices, all other governments

are indifferent to the outcome of its Step-2 choice problem. As small countries thus enjoy a degree

of sovereignty in their market access (Step-2) choices in the Multilateral Nash Policy game, we may

now state:

Proposition 9: The sovereignty of the government of a small country cannot be preserved in an

international agreement in which it is asked to make market access commitments.

Observe now that the best-response policy choices of the representative government c solve

for ,

which by (27) corresponds to the politically optimal policy choices for this government. Hence, if

a small country is not asked to make market access commitments in a trade agreement, it will

implement its politically optimal policies. Accordingly, by Propositions 6 and 9, international

efficiency can be consistent with preservation of the sovereignty of small countries only if MFN is

imposed. But by Proposition 7, MFN entails a (direct) sacrifice of national sovereignty over tariff

instruments. Referring to politically optimal market access agreements as market access agreements

which achieve the market access levels implied by politically optimal policies, we may now state:

Proposition 10: If some (but not all) countries are “small,” then achieving international efficiency

and preserving national sovereignty are mutually inconsistent goals. Politically optimal market

37

access agreements achieve international efficiency if they require governments to abide by the non-

discrimination rule, but this requirement directly compromises national sovereignty over tariff

instruments. International efficiency can be achieved without requiring governments to abide by the

non-discrimination rule, but only if the (Westphalian) sovereignty of small countries is compromised

so that market access levels which are efficient but not politically optimal may be achieved.

Proposition 10 identifies a direct tradeoff between international efficiency and national

sovereignty in a world in which some (but not all) countries are small. In effect, if small countries

are asked to make market access commitments, their Westphalian sovereignty in Step-2 choices will

be compromised. If this is to be avoided, then small countries must be left unconstrained to choose

their best-response policies in any international agreement. This requirement, though, is inconsistent

with international efficiency as long as discriminatory tariffs are permitted. A non-discrimination

rule is thus warranted on efficiency grounds, but entails its own (direct) sacrifice of national

sovereignty over tariff instruments. Nevertheless, the limited degree to which national sovereignty

must be sacrificed to achieve international efficiency in this setting is worth emphasizing, and so we

record it in the following:

Corollary: If some (but not all) countries are “small,” politically optimal market access agreements

that require governments to abide by the non-discrimination rule achieve international efficiency

while directly compromising national sovereignty over tariff instruments, but involve no further

sacrifice of national sovereignty.

In this sense, our three-country results suggest that a market access agreement coupled with a non-

discrimination rule can achieve international efficiency with minimal sacrifice of national

sovereignty.

VI. National Sovereignty and International Institutions

The essential logic from our analysis thus far boils down to a simple message: identify the

transmission mechanism of the international externality, write international agreements directly over

this transmission mechanism, and you can achieve international efficiency at the cost of a modest

8A more systematic exploration of national sovereignty in the case where important international externalities ofa non-pecuniary nature exist must consider how the presence of such externalities would affect the partitions of thegovernment choice problems that we have exploited in this paper. We leave this to future work.

38

(and possibly zero) sacrifice of national sovereignty. When the international externalities that create

international inefficiency are of a pecuniary nature, the transmission mechanism takes a specific

form: market access. What happens, though, when international externalities of a non-pecuniary

nature arise? In this section, we briefly explore one facet of this question.8

Specifically, we focus on an important distinction that arises between pecuniary and non-

pecuniary externalities. Pecuniary externalities give rise to inefficiency only if agents (in this case

governments) wield market power and can therefore affect prices (in this case world prices) with

their actions. In the case of non-pecuniary externalities, inefficiency typically arises even when all

agents are small and there is no market power affecting decisions.

The importance of this distinction for issues of national sovereignty can be appreciated by

noting that “small” countries by definition enjoy Westphalian sovereignty in all their decisions. In

the case of international pecuniary externalities, we have seen that small countries enjoy Westphalian

sovereignty in their market access choices of the Multilateral Nash Policy Game, while large

countries do not. But in a sense, where international pecuniary externalities are involved, it is also

the large countries – not the small – that are creating the inefficiency. This suggests that, in the case

of international pecuniary externalities, there is no inherent conflict between preserving Westphalian

sovereignty and achieving international efficiency through an international agreement, because only

the large countries need expand their market access beyond unilaterally chosen levels to achieve

international efficiency, and this requires of them no compromise of (Westphalian) sovereignty. This

suggestion is formalized in Propositions 5, 10 and their Corollaries.

In the case of international non-pecuniary externalities, however, a country will typically be

contributing to the international inefficiency even if it is “small” with regard to this externality, and

therefore even if it enjoys Westphalian sovereignty with respect to decisions that impact the

39

externality. This suggests that, in contrast to the case of international pecuniary externalities, when

important international non-pecuniary externalities are present, governments may face an inescapable

tradeoff between international efficiency and (Westphalian) sovereignty. This tradeoff is illustrated

most starkly in a hypothetical case where all countries are small in the dimension of an international

non-pecuniary externality. In that case, in the absence of an international agreement, all countries

enjoy Westphalian sovereignty in decisions that impact this externality. Nevertheless, even though

all countries are small, the existence of the international non-pecuniary externality typically creates

an international inefficiency, and the attainment of international efficiency therefore requires that

Westphalian sovereignty over decisions that impact this externality must be sacrificed.

This discussion suggests that, when it comes to issues of national sovereignty as they arise

in the context of efforts to solve international problems, not all international problems are alike. In

particular, international problems that reflect inefficiencies that are fundamentally driven by trade

have a particular structure – they concern international pecuniary externalities – which implies a

minimum of (or possibly even the absence of) inherent conflict between international efficiency and

national sovereignty. All other international problems – those that concern international non-

pecuniary externalities – pose a more direct efficiency/sovereignty tradeoff.

VII. Conclusion

What are the sovereign rights of nations in an interdependent world, and to what extent do

these rights stand in the way of achieving important international objectives? In this paper, we have

provided answers to these two questions. Our answers, of course, depend on the definition of

national sovereignty. We have formally defined two features of sovereignty – unilateral control and

internal affairs – that we believe are central to the respective notions of interdependence sovereignty

and Westphalian sovereignty emphasized in the political science literature. And using these

definitions, we have shown how Nash choice problems can be partitioned in a way that allows a

characterization of the degree and nature of sovereignty that governments possess in the Nash

equilibrium. This characterization, in turn, provides a benchmark from which to formally assess the

implications for national sovereignty of international agreements of various designs. In regard to

40

this assessment, we report two broad findings.

First, in the context of international commercial relations, we find that in principle there is

no inherent conflict between the twin objectives of attaining international efficiency through

international agreements and preserving national sovereignty. And we find that a number of the

foundational aspects of the GATT/WTO, such as its emphasis on market access commitments and

the MFN rule, are in harmony with these twin objectives. In this regard, we give formal support to

the observation of Rabkin (1998):

“Probably the single most effective and consequential international program of the postwar era has been the mutualreduction of trade barriers under the General Agreement on Tariffs and Trade, initiated in 1947. Reasonable questionsmay be raised about certain aspects of the World Trade Organization, established in 1995 to help administer GATTnorms. But, fundamentally, the trading system is quite compatible with traditional notions of sovereignty. It wasdeveloped on the foundations of much older sorts of international agreement, which would have been quite recognizableto the Framers of the Constitution.” Rabkin, pp. 85-86.

However, our results also suggest that the maintenance of this compatibility depends crucially on

being true to these fundamental principles: the further away the WTO moves from a market-access

focus and adherence to MFN, the more likely will conflicts arise within the WTO between

international efficiency and national sovereignty.

Our second broad finding is that, in the universe of international relations among national

governments, commercial relations are special, because trade problems that warrant international

attention reflect international externalities of a pecuniary nature. Pecuniary externalities give rise

to a distinctive structure that, as we have demonstrated, suggests a natural harmony between national

sovereignty and international efficiency. In contrast, to the extent that governments are

interdependent as a result of non-pecuniary externalities, we suggest that the conflicts between

international efficiency and national sovereignty may be inescapable.

41

References

Bagwell, Kyle, and Robert W. Staiger, “An Economic Theory of GATT,” American Economic

Review, March 1999.

Bagwell, Kyle, and Robert W. Staiger, “Domestic Policies, National Sovereignty and International

Economic Institutions,” Quarterly Journal of Economics, May 2001.

Bagwell, Kyle, and Robert W. Staiger, “The WTO as a Mechanism for Securing Market Access

Property Rights: Implications for Global Labor and Environmental Issues,” Journal of

Economic Perspectives, Summer 2001.

de Vattel, Emmerich, The Law of Nations, Translated by Joseph Chitty, T.& J. W. Johnson & Co.,

Law Booksellers, Philadelphia. 1872.

Krasner, Stephen D. Sovereignty: Organized Hypocrisy, Princeton University Press. 2001.

Rabkin, Jeremy, Why Sovereignty Matters, The AEI Press, Washington D.C.. 1998.

42

Appendix

In this Appendix, we provide proofs of all lemmas and propositions that are not proved in

the body of the paper.

Lemma 1: Program 1 and Program 1' are equivalent ways of characterizing the domestic

government’s best-response policies for any and .

Proof: We prove this by establishing that the first-order conditions associated with Program 1', (13)-

(16), are equivalent to the first-order conditions associated with Program 1, (5)-(6). To establish this,

we first use (3) to derive

.

With this expression, and using (15) and (16) to eliminate from (14) , it is then direct to verify that

(6) and (14) are equivalent. Similarly, we use (3) to derive

for .

With this expression, and using (15) and (16) to eliminate from (13), it is then direct to verify that

(5) and (13) are equivalent. QED

Proposition 6: Politically optimal tariffs and regulations are efficient if and only if the tariffs

conform to MFN. Moreover, if any country sets its politically optimal policies, then efficiency

requires that all countries set their politically optimal policies and abide by MFN.

Proof: To prove this proposition, we first characterize the efficiency frontier of the 3-country model.

To this end, fix foreign welfare levels for and define implicitly by

for .

Observe that

43

(A1) ; and ,

for and . We may now define

,

and observe that, by the market-clearing condition (21), a value of is implied, which we denote

by . We may thus write domestic government welfare as a function of the

domestic regulatory choices, the foreign regulatory choices and foreign tariffs, and the foreign

welfare levels, or

(A2) .

Fixing foreign welfare levels and choosing domestic and foreign regulations and foreign tariffs to

maximize domestic welfare given by (A2) then defines a point on the efficiency frontier. The first

order conditions that define the efficiency frontier are

(A3) for ,

(A4) for and , and

(A5) for .

By (27) and (A3)-(A5), politically optimal tariffs and regulations are efficient if and only if

(A6) for and .

But by (A1), (A6) is satisfied at the political optimum if and only if

(A7) for and .

Hence, by (A7), politically optimal tariffs and regulations are efficient if and only if the tariffs

44

conform to MFN (so that for ). Further, if any country’s policies are set at their

politically optimal levels, then (A1)-(A7) can be used to show that efficiency requires that all

countries set their politically optimal policies and abide by MFN. QED

Lemma 3: Program 3 and Program 3' are equivalent ways of characterizing the domestic

government’s best-response policies for any , , and .

Proof: We prove this by establishing that the first-order conditions associated with Program 3', (30)-

(32), are equivalent to the first-order conditions associated with Program 3, (23)-(26). To this end,

we first use (30) and (32) to derive an expression for , which allows (29) to be written as

(A8) .

Next, we observe that (24) implies , which can be manipulated to yield

(A9) ,

which in turn allows to be written as

(A10) .

Using the linkage condition (18) and the market-clearing condition (21), expressions for

and may be derived which, when substituted into (A10), yield

(A11) .

Therefore, by substituting (A11) into (24) and observing that the resulting expression is identical to

(A8), we may conclude that (30), (32) and (29) imply (24). Similarly, we use (30) and (31) to derive

an alternative expression for , which allows (28) to be written as

(A12) .

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Now using (18) and (21), we may derive that

(A13) .

Substituting (A13) into (A12) yields an expression identical to (23). Hence, we may conclude that

(30), (31) and (28) imply (23). QED